The population of ants in the colony can be represented by the function
f(t) = 1400(1.07), where t is the number of months the colony has been
measured.
What is the growth rate??

The percentage of the variation in y can be explained by the corresponding variation in x and the least - squares line

The value of the coefficient of determination r2 = 0.9617*0.9617 = 0.9249

percentage of the variation in y can be explained by the corresponding variation in x and the least - squares line is = 92.49%

So, percentage is unexplained = (100 - 92.49)%

= 7.51%

Therefore, the percentage of the variation in y that can be explained by the corresponding variation in x and the least-squares line is 92.49% . The percentage which is unexplained is 7.51% i.e. (100%−92.49%) .

Hence the variation in X and the least-squares line is 7.51%

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The perimeter of the parallelogram ABCD is, 58 units.

What is perimeter?

The length of a shape's boundary taken as a whole is referred to as its perimeter. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

Consider the given vertices, A(1, 1), B(17, 1), C(22, 13), D(6, 13).

The perimeter of parallelogram is the sum of all sides of parallelogram.

So, first to find the length of each side of parallelogram, using the distance formula,

[tex]d = \sqrt{(x_2 -x_1)^2+(y_2-y_1)^2}[/tex]

So,

[tex]AB = \sqrt{(17-1)^2+(1-1)^2}=\sqrt{16^2-0} = 16\\ BC = \sqrt{(22-17)^2+(13-1)^2} = \sqrt{5^2+12^2}= \sqrt{25+144}=13\\ CD = \sqrt{(6-22)^2+(13-13)^2} = \sqrt{16^2+0}=16\\ AD = \sqrt{(6-1)^2+(13-1)^2}=\sqrt{5^2+12^2} =\sqrt{25+144}=13[/tex]

Therefore, the perimeter of the parallelogram ABCD is,

P = AB + BC + CD + AD

P = 16 + 13 + 16 + 13

P = 58

Hence, the perimeter of  the parallelogram ABCD is, 58 units.

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The postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.

First, let us understand the congruency of the triangle:

When two triangles have the same sides and angles, they are congruent. That is, one's three sides are equal to the other's three sides, and one's three angles are equal to the angles of the other.

In triangles ABD and CBD;

Side BD = side BD (common)

∠ABD = ∠CBD (90 degrees)

Side AB = side CB (common)

For this triangle pair, the postulate that fit are:

SAS since the two sides and the included angle are equal in both triangles.

Thus, the postulate which can be used to prove that the given triangles are congruent is SAS. Option A is correct.

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Answer:

GCF = 7

Step-by-step explanation:

The greatest common factor is equal to the product of the prime factors that all of the original numbers have in common.

The greatest common factor of 49, 21 and 49 is 7.

The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is

x = 12 or x = -6

What is a quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

The given quadratic equation is

[tex]x^2 - 6x = 72[/tex]

Now,

[tex]x^2 - 6x = 72\\x^2 - 6x - 72 = 0\\x^2 - 12x + 6x -72 = 0\\x(x -12)+6(x -12)=0\\(x-12)(x+6)=0\\x-12=0 \ or \ x+6 = 0\\x = 12 \ or \ x = -6[/tex]

The solution of the quadratic equation [tex]x^2 - 6x = 72[/tex] is

x = 12 or x = -6

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Answer:

0.75

Step-by-step explanation:

because 9/12 is 0.75

Let's establish what this rate indicates through an equation:

inches burned

       hour

Now, plug in the information you have:

inches burned      =          9

       hour                          12

9/12 = 0.75

0.75 inches of the candle is burned per hour

Answer: 0.83

Step-by-step explanation:

14.5/17.5 = 0.828571429

We stop at the 2nd decimal placement after 0.82 but because the following number 8 > 0 we round up the hundredths place which gives us 0.83

60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

According to the question,

We have the following information:

3 digits integers are to be made from 1,2,3,4 and 5

So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.

Now, we have:

Total number of digits = 5

Number of digits to be made = 3

So, we have:

[tex]^{5} P_{3}[/tex]

Solving this expression:

5*4*3

60

Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.

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Answer: 0.06 repeated, I'm sorry if it's wrong! I used a calculator.

Step-by-step explanation:

Calculating 2 divided by 5 / 6 should give you the answer 0.06666666666.

Answer:

Step-by-step explanation:

Answer:

Hotdogs: $12

Buns: $6

Altogether (Hotdogs plus Buns): $18

Step-by-step explanation:

She wants 48 hot dogs, and each package contains 8 hotdogs.

48/8 = 6

She'd have to buy 6 packages

6 packages x $2 each = $12

She'd be spending $12 on the hotdogs

She'd also have to get an equivalent amount of buns

Each bag has 12 buns. She needs 48 buns.

48 buns /12 per bag = 4 bags

She would need to buy 4 bags of buns

$1.50 per bag x 4 bags = $6

She'd be spending $6 on buns

Adding the amount she spends on both the buns and hotdogs, she spends $18

The sequence of transformations is described as follows:

B. Reflection over the y-axis, translation 6 units right and 4 units up, dilation with center (0,0) and scale factor 2.

The two polygons have vertical symmetry, hence the reflection was over the y-axis.

Two equivalent vertices are given as follows:

R(4,-4) and V(2,-4).

After the reflection over the y-axis, the coordinates would be of:

R'(-2,-4).

The polygon increases after the transformation, hence the dilation has a scale factor greater than 1, which is of 2, as VZ = 8, RU = 4.

With a dilation with scale factor of 2, the coordinates of R'' would be given as follows:

R''(-4,-8).

The coordinates of V are:

(2,-4).

Hence the translation is:

Hence option B is correct.

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Solving by the system of linear equations, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.

What do you mean by system of linear equations?

A system of linear equations consists of two or more equations, each of which has two or more variables, and all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy each of the system's linear equations is necessary to identify the system's unique solution.

Let, the cost per pound of peanut be $x and for M&M's be y

so, according to the question, we are getting two linear equations,

$8x + $5y = $55.27..................(i)

$6x + $4y = $42.70....................(ii)

Solving this two systems of linear equations , x=$3.79 and y=$4.99

Hence, the Cost per pound of peanuts is $3.79 and M&M's is $4.99.

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Answer:log base 2 of the quantity x cubed z squared all divided by y to the fourth end log

Step-by-step explanation:

Answer:

y÷3

Step-by-step explanation:

y/3 is the same as y÷3

Answer:

3340 miles

Step-by-step explanation:

Multiply 4x835=3340 miles

The decimal division of 18.92 by 11 gives us; 1.72

When dividing decimals  we first of all have to convert the divisor to a whole number by moving the decimal point to the right. Thereafter, we now carry the dividend's decimal point up to the exact same number of places to the right and then divide the resultant numbers in the normal way like in regular long division.

We want to divide 18.92 by 11. Thus, let us apply that rule described above to get;

18.92/11 = 1892/1100

= 1 + (1892 - 1100)/1100

= 1 + (792/1100)

= 1 + 0.72

= 1.72

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The measure of the interior angle adjacent to the sixth exterior angle of the heaxagon is 118°.

Interior angles are those that lie inside a polygon.

To calculate an interior angle of a hexagon, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

Recall that, the sum of an interior and exterior angle is 180°

Where:

Substitute the value of a into equation 2

Hence, the value of the interior angle is 118°.

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A new company wants to offer a line queuing service where customers book someone to wait in line on their behalf through a smart phone app.

The possibility that no one wants to pay someone else to wait in line can be represented by the concept of probability.

The probability of an event occurring is defined by probability.

The outcome of an event may be known to us or unknown to us. When this happens we say that there is a chance that the event will happen or not.

We can identify probability by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

Hence, probability is a numerical representation of the chance that a specific event will take place.

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The measure of angles ∠1 = 60 degrees, ∠2=120 degrees, ∠3 = 60 degrees, ∠4=60 degrees, ∠5 = 120 degrees, ∠6= 120degreesa and ∠7 = 60 degrees

The measure of angle 3 = 180 - 120

= 60 degrees

Because the sum of angles on a straight line will be 180 degrees

The measure of angle 6 = 120 degrees

The measure of angle 3 = The measure of angle 7  = 60 degrees

Because the corresponding angle will be equal

The measure of angle 1 = 180-120

= 60 degrees

The measure of angle 2 = 180 - 60

= 120 degrees

Because the sum of angles on a straight line will be 180 degrees

The measure of angle 2 = The measure of angle 5 = 120 degrees

The measure of angle 1 = The measure of angle 4 = 60 degrees

Because the corresponding angles will be equal

Hence, the measure of angles ∠1 = 60 degrees, ∠2=120 degrees, ∠3 = 60 degrees, ∠4=60 degrees, ∠5 = 120 degrees, ∠6= 120degrees and ∠7 = 60 degrees

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The measure of  ∠x is 190°

Define Exterior angle

In the given diagram, all angles marked is an exterior angle

And, we know sum of exterior angle is 360°

So, now just equate the given values to 360 degree

x + 60 + 110 = 360

x + 170 = 360

x = 360 - 170

x = 190°

Hence, the measure of ∠x is 190°

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There are 2730 ways in which 15 race cars can finish in first, second, and third place.

Let's examine this logically now. Any one of the 15 runners can cross the finish line in first place. You can still have any one of the 14 race cars who are still running finish in second place. Any one of the 13 race cars who haven't crossed the finish line yet can take third place.

As a result, multiplying all the possibilities will give us the number of ways ;

Number of ways =15*14*13

                            =2730

So, the total number of ways in which the race cars finish in first, second, and third place is 2730.

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Answer:250

Step-by-step explanation:5((6(8))+2)=250 using pemdas start with parenthesis so 6*8=48 this puts the equation at 5(48+2) then do the parenthesis again so 48+2=50 this puts the equation at 5*50 then do your last step which will give you your answer of 250

Answer:

  x = 42

Step-by-step explanation:

You want to know the value of x that makes alternate interior angles 105° and (3x-21)° congruent.

When alternate interior angles are congruent, the lines forming them are parallel. Congruent angles have the same measure, so we want ...

  3x -21 = 105

  3x = 126 . . . . . . add 21

  x = 42 . . . . . . . divide by 3

The value of x is 42 when the lines are parallel.

Alexander made $742 last week in commission. He made $40068 in commission in 2011.

Sold = $5300

Commission percent = 14%

Commission = 14% of 5300

                     = (14/100)*5300

                     = 14*53

                     = 742

No. of weeks in 2011 = 54

Commission = 54 * 742

                     = 40068

Hence, he makes $742 in weeks and $40068 in year 2011.

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Given that the directrix is -2 and the vertex is  (-4,-3), the graph will be the parabola plotted in the negative quadrant.

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. Three crucial components make up a parabola: a focus, a directrix, and a vertex. This upward-opening parabola illustrates how all points along its curve will be equally distant from the directrix and the focus.

Here,

The equation of the parabola is,

f(x)=-2(x+4)²-3

a=-2

(h,k)=(-4,-3)

The graph will be the parabola plotted in the negative quadrant as the directrix is -2. and the vertex is (-4,-3).

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Answer:

y(y+27)

Step-by-step explanation:

as per it is y2 it is two times counted so

y(y+27)

Answer:

x=20

x= -20

Step-by-step explanation: